The first \(2^{+}\) excited states of the nucleus directly reflect the interaction between the shell structure and the nucleus, providing insights into the validity of the shell model and nuclear structure characteristics. Although the features of the first \(2^{+}\) excited states can be measured for stable nuclei and calculated using nuclear models, significant uncertainty remains. This study employs a machine learning model based on a light gradient boosting machine (LightGBM) to investigate the first \(2^{+}\) excited states. Specifically, the training of the LightGBM algorithm and the prediction of the first 2 \(^{+}\) properties of 642 nuclei are presented. Furthermore, detailed comparisons of the LightGBM predictions were performed with available experimental data, shell model calculations, and Bayesian neural network predictions. The results revealed that the average difference between the LightGBM predictions and the experimental data was 18 times smaller than that obtained by the shell model and only 70% of the BNN prediction results. Considering Mg, Ca, Kr, Sm, and Pb isotopes as examples, it was also observed that LightGBM can effectively reproduce the magic number mutation caused by shell effects, with the energy being as low as 0.04 MeV due to shape coexistence. Therefore, we believe that leveraging LightGBM-based machine learning can profoundly enhance our insights into nuclear structures and provide new avenues for nuclear physics research.
